Upper bounds on the error probability of channel coding are derived for codebooks drawn from random codebook ensembles with various independence and symmetry assumptions. For regular decoding (without an erasure option), the random coding union bound of Polyanskiy et al. is improved by carefully taking ties (equal likelihood scores) into account. It is shown that the improved bound is always better than threshold-decoding based bounds. The framework is extended to the case of decoding with an erasure option, deriving several achievability bounds in the same spirit. In order to exemplify the merits of the approach, the bounds are evaluated for the case of pairwise-independent uniformly-distributed ensembles (e.g., shifted random linear codes).

In this paper, we obtain an improved lower bound on the error exponent of the memoryless multiple-access channel via the use of linear codes, thus demonstrating that structure can be beneficial even when capacity may be achieved via random codes. We show that if the multiple-access channel is additive over a finite field, then any error probability, and hence any error exponent, achievable by a linear code for the associated single-user channel, is also achievable for the multiple-access channel. In particular, linear codes allow to attain joint expurgation, and hence, attain the single-user expurgated exponent of the single-user channel, whenever the latter is achieved by a uniform distribution. Thus, for additive channels, at low rates, where expurgation is needed, our approach strictly improves performance over previous results, where expurgation was used for at most one of the users. Even when the multiple-access channel is not additive, it may be transformed into such a channel. While the transformation is information-lossy, we show that the distributed structure gain in some “nearly additive” cases outweighs the loss. Finally, we apply a similar approach to the Gaussian multiple-access channel. While we believe that due to the power constraints, it is impossible to attain the singleuser error exponent, we do obtain an improvement over the best known achievable error exponent, given by Gallager, for certain parameters. This is accomplished using a nested lattice triplet with judiciously chosen parameters.

We consider the problem of distributed binary hypothesis testing of two sequences that are generated by a doubly binary symmetric source. Each sequence is observed by a different terminal. The two hypotheses correspond to different levels of correlation between the two source components, i.e., the i.i.d. probability of the difference between the two sequences. The terminals communicate with a decision function via equal-rate noiseless links. We analyze the tradeoff between the exponential decay of the error probabilities of the hypothesis test and the communication rate. As Körner-Marton coding is known to minimize the rate in the corresponding distributed compression problem of conveying the difference sequence, it constitutes a natural candidate for the present setting. Indeed, using this scheme we derive achievable error exponents. Interestingly, these coincide with part of the optimal tradeoff without communication constraints, even when the rate is below the Körner-Marton rate for one of the hypotheses.

Upper bounds on the error probability in channel coding are considered, improving the RCU bound by taking into account events, where the likelihood of the correct codeword is tied with that of some competitors. This bound is compared to various previous results, both qualitatively and quantitatively; it is shown to be the tightest bound with respect to previous bounds with the same computational complexity. With respect to maximal error probability of linear codes, it is observed that when the channel is additive, the derivation of bounds, as well as the assumptions on the admissible encoder and decoder, simplify considerably.

We consider the error exponent of the memoryless multiple-access (MAC) channel. We show that if the MAC channel is modulo-additive, then any error probability, and hence any error exponent, achievable by a linear code for the corresponding single-user channel, is also achievable for the MAC channel. Specifically, for an alphabet of prime cardinality, where linear codes achieve the best known exponents in the single-user setting (and the optimal exponent above the critical rate), this performance carries over to the MAC setting. At least at low rates, where expurgation is needed, our approach strictly improves performance over previous results, where expurgation was used at most for one of the users. Even when the MAC channel is not additive, it may be transformed into such a channel. While the transformation is lossy, we show that the distributed structure gain in some “nearly additive” cases outweighs the loss, and thus we can improve upon the best known exponent for these cases as well. This approach is related to that previously proposed for the Gaussian MAC channel, and is based on “distributed structure”.

Structured codes have been utilized in deriving the best known achievable rate regions in certain network scenarios. In this paper we demonstrate that structure can be also beneficial in terms of error exponents even in cases where there is no capacity gain. We use distributed structure, i.e., different users use codes which satisfy a nesting condition. Specifically, for the scalar Gaussian multiple-access channel we obtain an improvement over the best known achievable exponent, given by Gallager, for certain rate pairs.

We study cost constrained side-information channels, where the cost function depends on a state which is known only to the encoder. In the additive noise case, we bound the capacity loss due to not knowing the cost state at the decoder and show that it is small under various assumptions, and goes to zero in the limit of weak noise. This model plays an important role in the (non-degraded) broadcast channel. In the semi-additive noise case, we bound the gap between the best known single letter achievable region and the true capacity region, using tools developed for the first problem. In the limit of weak noise, we show that the bounds coincide, thus we get the complete characterization of the capacity region.